def __init__(self, α: np.ndarray, z: np.ndarray, bor: float):
"""
:param α: sufficient statistics of the posterior Dirichlet density on model/family frequencies
:param z: posterior probabilities for each subject to belong to each model/family
:param bor: Bayesian omnibus risk p(y|H0)/(p(y|H0)+p(y|H1))
"""
self.attribution = z.copy()
self.frequency_mean = dirichlet.mean(α)
self.frequency_var = dirichlet.var(α)
self.exceedance_probability = exceedance_probability(dirichlet(α))
self.protected_exceedance_probability = self.exceedance_probability * (
1 - bor) + bor / len(α) # (7)
def test_frozen_dirichlet():
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
assert_equal(d.var(), dirichlet.var(alpha))
assert_equal(d.mean(), dirichlet.mean(alpha))
assert_equal(d.entropy(), dirichlet.entropy(alpha))
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
assert_equal(d.pdf(x[:-1]), dirichlet.pdf(x[:-1], alpha))
assert_equal(d.logpdf(x[:-1]), dirichlet.logpdf(x[:-1], alpha))
n_samples = 10000
# Observed Data
count_obs = OrderedDict({'id1': 87, 'id2': 34, 'id3': 1})
counts = np.array(list(count_obs.values()), dtype=int)
dirichlet_prior = np.ones_like(
counts) # uninformative prior based on pseudo-counts
dirichlet_posterior = dirichlet_prior + counts
prior_samples = get_samples(dirichlet_prior)
posterior_samples = get_samples(dirichlet_posterior)
print('prior means: %s' % (str(dlt.mean(dirichlet_prior))))
PoM = dlt.mean(dirichlet_posterior)
print('posterior means: %s' % (str(PoM)))
PoV = dlt.var(dirichlet_posterior)
print('posterior variances: %s' % (str(PoV)))
print('naive posterior means: %s' % ((counts + 1) / np.sum(counts + 1))
) # expected from value counts plus assumed prior counts
print('Entropy DLT prior:', dlt.entropy(dirichlet_prior))
print('Entropy DLT posterior:', dlt.entropy(dirichlet_posterior))
if plot_priors:
plt.figure(figsize=(9, 6))
for i, label in enumerate(count_obs.keys()):
ax = plt.hist(prior_samples[:, i],
bins=50,
density=True,
alpha=.35,
label=label,
histtype='stepfilled')
def compute_LPV_from_parameters(alpha_vector):
M = dlt.mean(alpha_vector)
V = dlt.var(alpha_vector)
LPV = M - 1.65 * np.sqrt(V) # 5-percentile
return np.where(LPV < 0, 0, LPV)
def var(self):
return dirichlet.var(self.alpha)